Approximate-likelihood Bayesian computation (ABC) approaches
[1]}, [2]} have become popular in situations where it is
not possible (or undesirable) to derive and compute the likelihood function of
a model.
The basic idea is simple: by generating simulations under the model, the
fraction of times that we generate a simulated dataset that matches the
observed data is a Monte Carlo approximation of the likelihood.
Because simulating the observed data exactly is often not possible (or extremely
unlikely), simulations “close enough” to the observed data are
counted, and usually a set of insufficient summary statistics are used in place
of the data.
Whether a simulated dataset is “close enough” to count is formalized as
whether or not it falls within a zone of tolerance around the empirical data.
